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A self-excited system is a nonlinear system with the property that a constant input yields a bounded, nonconvergent response. Nonlinear identification of self-excited systems is considered using a Lur'e model structure, where a linear model is connected in feedback with a nonlinear feedback function. To facilitate identification, the nonlinear feedback function is assumed to be continuous and piecewise affine (CPA). The present paper uses least-squares optimization to estimate the coefficients of the linear dynamics and the slope vector of the CPA nonlinearity, as well as mixed-integer optimization to estimate the order of the linear dynamics and the breakpoints of the CPA function. The proposed identification technique requires only output data, and thus no measurement of the constant input is required. This technique is illustrated on a diverse collection of low-dimensional numerical examples as well as data from a gas-turbine combustor. 

This paper considers system identification for systems whose output is asymptotically periodic under constant inputs. The model used for system identification is a discretetime Lur’e model consisting of asymptotically stable linear dynamics, a time delay, a washout filter, and a static nonlinear feedback mapping. For sufficiently large scaling of the loop transfer function, these components cause divergence under small signal levels and decay under large signal amplitudes, thus producing an asymptotically oscillatory output. A leastsquares technique is used to estimate the coefficients of the linear model as well as the parameters of a piecewise-linear approximation of the feedback mapping. 

Identification of self excited systems 

Description of the DISCo facility and adaptive control experiments 

Self-excited systems arise in many applications, such as biochemical systems, mechanical systems with fluidstructure interaction, and fuel-driven systems with combustion dynamics. This paper presents a Lur’e model that exhibits biased oscillations under constant inputs. The model involves arbitrary asymptotically stable linear dynamics, time delay, a washout filter, and a saturation nonlinearity. For all sufficiently large scalings of the loop transfer function, these components cause divergence under small signal levels and decay under large signal amplitudes, thus producing an oscillatory response. A bias-generation mechanism is used to specify the mean of the oscillation. The main contribution of the paper is the presentation and analysis of a discrete-time version of this model.